Compressible fluids driven by stochastic forcing: The relative energy inequality and applications

TL;DR

This paper establishes a relative energy inequality for stochastic compressible Navier-Stokes equations, leading to weak-strong uniqueness, convergence results, and a Yamada-Watanabe type theorem in this context.

Contribution

It introduces a relative energy inequality for stochastic compressible fluids and proves weak-strong uniqueness and convergence, extending classical results to stochastic systems.

Findings

Proved relative energy inequality for stochastic compressible Navier-Stokes.

Established weak-strong uniqueness both pathwise and in law.

Demonstrated convergence in the inviscid-incompressible limit.

Abstract

We show the relative energy inequality for the compressible Navier-Stokes system driven by a stochastic forcing. As a corollary, we prove the weak-strong uniqueness property (pathwise and in law) and convergence of weak solutions in the inviscid-incompressible limit. In particular, we establish a Yamada-Watanabe type result in the context of the compressible Navier-Stokes system, that is, pathwise weak--strong uniqueness implies weak--strong uniqueness in law.